Traveling Salesman: Minimum Spanning Tree

April 13, 2010

We looked at the traveling salesman problem in two previousexercises. We also studied twoalgorithms for computing the minimum spanning tree. In today’s exercise, we will use a minimum spanning tree as the basis for computing a traveling salesman tour.

It is easy to convert a minimum spanning tree to a traveling salesman tour. Pick a starting vertex on the minimum spanning tree; any one will do. Then perform depth-first search on the tree rooted at the selected vertex, adding each vertex to the traveling salesman tour as it is selected. The resulting tour is guaranteed to be no longer than twice the optimal tour. Considering the speed of the algorithm, that’s a pretty good result.

Your task is to write a program that finds traveling salesman solutions using a minimum spanning tree as described above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.